# A random sample of 378 married

A random sample of 378 married couples found that 300 had two or more personality preferences in common. In another random sample of 580 married couples, it was found that only 20 had no preferences in common. Let p1 be the population proportion of all married couples who have two or more personality preferences in common. Let p2 be the population proportion of all married couples who have no personality preferences in common.

(a) Find a 90% confidence interval for p1 – p2. (Use 3 decimal places.)

 lower limit upper limit

# A random sample of 378 married

A random sample of 378 married couples found that 300 had two or more personality preferences in common. In another random sample of 580 married couples, it was found that only 22 had no preferences in common. Let p1 be the population proportion of all married couples who have two or more personality preferences in common. Let p2 be the population proportion of all married couples who have no personality preferences in common.

(a) Find a 90% confidence interval for p1 – p2. (Use 3 decimal places.)

 lower limit upper limit

(b) Explain the meaning of the confidence interval in part (a) in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you (at the 90% confidence level) about the proportion of married couples with two or more personality preferences in common compared with the proportion of married couples sharing no personality preferences in common?

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